This work concerns the application of new computer architectures to the creation and manipulation of high-quality audio bandwidth signals. The configuration of both the hardware and software in such systems falls under consideration in the three major sections which present increasing levels of algorithmic concurrency. In the first section, the programs which are described are distributed in identical copies across an array of processing elements; these programs run autonomously, generating data independently, but with control parameters peculiar to each copy: this type of concurrency is referred to as isonomic}The central section presents a structure which distributes tasks across an arbitrary network of processors; the flow of control in such a program is quasi- indeterminate, and controlled on a demand basis by the rate of completion of the slave tasks and their irregular interaction with the master. Whilst that interaction is, in principle, deterministic, it is also data-dependent; the dynamic nature of task allocation demands that no a priori knowledge of the rate of task completion be required. This type of concurrency is called dianomic? Finally, an architecture is described which will support a very high level of algorithmic concurrency. The programs which make efficient use of such a machine are designed not by considering flow of control, but by considering flow of data. Each atomic algorithmic unit is made as simple as possible, which results in the extensive distribution of a program over very many processing elements. Programs designed by considering only the optimum data exchange routes are said to exhibit systolic^ concurrency. Often neglected in the study of system design are those provisions necessary for practical implementations. It was intended to provide users with useful application programs in fulfilment of this study; the target group is electroacoustic composers, who use digital signal processing techniques in the context of musical composition. Some of the algorithms in use in this field are highly complex, often requiring a quantity of processing for each sample which exceeds that currently available even from very powerful computers. Consequently, applications tend to operate not in 'real-time' (where the output of a system responds to its input apparently instantaneously), but by the manipulation of sounds recorded digitally on a mass storage device. The first two sections adopt existing, public-domain software, and seek to increase its speed of execution significantly by parallel techniques, with the minimum compromise of functionality and ease of use. Those chosen are the general- purpose direct synthesis program CSOUND, from M.I.T., and a stand-alone phase vocoder system from the C.D.P.(^4). In each case, the desired aim is achieved: to increase speed of execution by two orders of magnitude over the systems currently in use by composers. This requires substantial restructuring of the programs, and careful consideration of the best computer architectures on which they are to run concurrently. The third section examines the rationale behind the use of computers in music, and begins with the implementation of a sophisticated electronic musical instrument capable of a degree of expression at least equal to its acoustic counterparts. It seems that the flexible control of such an instrument demands a greater computing resource than the sound synthesis part. A machine has been constructed with the intention of enabling the 'gestural capture' of performance information in real-time; the structure of this computer, which has one hundred and sixty high-performance microprocessors running in parallel, is expounded; and the systolic programming techniques required to take advantage of such an array are illustrated in the Occam programming language.